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1.计算5a/(6a^2c)-7b/(12ac^2)+11c/8a^2b

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1.计算5a/(6a^2c)-7b/(12ac^2)+11c/8a^2b
2.计算[y/(x^2-xy)+x(y^2-xy)]/(xy)
3.计算{(b-c)/[(a-b)(a-c)]}+{(a-c)/[(b-a)(b-c)]}+{(a-b)/[(c-a)(c-b)]}
4.已知3x/(x^2-1)=A/(x+1)+B/(x-1),求A、B的值.
1.计算5a/(6a^2c)-7b/(12ac^2)+11c/8a^2b
(1) 5a/(6a^2c)-7b/(12ac^2)+11c/8a^2b =(20abc-14a^2b+33c^3)/(24a^2bc^2) (2) [y/(x^2-xy)+x(y^2-xy)]/(xy) =((y^2-x^2)/(xy(x-y))/(xy) =-(x+y)/(x^2y^2) (3) {(b-c)/[(a-b)(a-c)]}+{(a-c)/[(b-a)(b-c)]}+{(a-b)/[(c-a)(c-b)]} =(-(b-c)^2-(a-c)(c-a)-(a-b)^2)/((a-b)(b-c)(c-a)) =2(ab+bc-ac-b^2)/((a-b)(b-c)(c-a)) (4) 3x/(x^2-1)=A/(x+1)+B/(x-1)=(A(x-1)+B(x+1)/((x+1)(x-1)) =((A+B)x+(B-A))/*x^2-1) 上式对任何x成立 所以:A+B=3 B-A=0 所以:A=3/2,B=3/2